I suggest you ...

Have option for KeePassDroid go into background once you copy password to clipboard

Once the password has been copied to the clipboard, I'm looking to switch over to another application to input that password. Having the option of making KeePassDroid jump into the background would save the step(s) of backing out of the application & switching over to the other application.

This would indeed be a very nice feature.
My specific use case is:
For example, Im in Settings->Accounts&Sync->Add account..., then when Im prompted for the password, I use SwipePad to start KeePassDroid. Then I copy the password to clipboard, but now there is no easy way back to "Accounts&Sync". (Long-pressing "Home" basically works, but in this specific case it will only take you back to "Settings", not "Accounts&Sync", and some information you might already have entered in "Accounts&Sync" is lost.)

This is an example where it would be extremely useful if KeePassDroid auto-"minimized" itself when the password (or username) is copied, to bring the last active app to the foreground.
Especially when used in conjunction with SwipePad, this would be very handy.

If you are using any recent version of android (I think 2.0+, possibly earlier), you should be able to long-press the home button and get a list of recently used apps, one of which will likely be the one you need to paste into. This also works to switch BACK to KPD afterwards.